Add simulate of analytic case for DefaultMixedNewAPI

[JerryChen97]

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Context:
The implementation of method simulate is the most important one under the architecture of new API standard. The point of simulate, is basically abstract both the analytic version (controlled by shots=None, or infinite shots in a fancier way) and the MC version (finite shots). Meanwhile, the functionality of such method should not truly depend on our details of qml implementationi; they better only rely on either the fundamental computation libs, e.g. math lib and qnp, or the most essential infras, e.g. Tape/Scripts and Operations.

Description of the Change:

Benefits:

Possible Drawbacks:

Related GitHub Issues:
[sc-73320]

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